Father of Padma Lakshmi's Child Seeks Greater Custody

Custody drama is back on the front burner for Top Chef host Padma Lakshmi.

Adam Dell, the father of Lakshmi's 11-month-old daughter Krishna Thea, having long been unhappy with the custody arrangement hammered out last spring, has now filed court papers in Manhattan seeking more time with Krishna.

"Adam wanted to avoid going to court, but it was so frustrating trying to find a co-parenting agreement [that] he had to take this action," a source close to Dell tells PEOPLE. "He's seeking sole custody of his daughter – but he's hoping for a shared custody agreement." The source adds that in New York, courts are not authorized to grant joint custody, which is why Dell has filed for sole custody.

Custody arrangements have been a source of tension between Lakshmi and Dell ever since Krishna's arrival last February. Dell, a venture capitalist who was finally revealed as Krishna's father in March, has been said to want more involvement with his daughter all along.

According to the source, Dell now gets to see Krishna for seven hours a week. "He's allowed nine visits a month and no longer than three and half hours," the source says, adding that scheduling visitation is sometimes difficult as Lakshmi travels often for work.

Lakshmi, 40, who is said to want nothing to do with Dell beyond his role as Krishna's biological father, has been forced to fend off accusations that she is not giving Dell the access to Krishna that he wants.

"Ms. Lakshmi believes that family matters should be kept private," reads a statement released by her rep. "She asks that those who join her in wanting the best for her daughter do the same. Twenty-four hours after the NY Post was told about Adam Dell's lawsuit, neither Padma Lakshmi nor her lawyers had received a copy of it; they only learned of it through a statement Mr. Dell provided to the press. Ms. Lakshmi's sole interest lies in preserving the privacy and welfare of her daughter and in working out and fair and amicable agreement out of the media's glare."

But Dell's attorney says his client isn't interested in garnering attention. "Adam is not seeking publicity," his lawyer, Bill Zabel, of Manhattan law firm Schulte, Roth & Zabel, tells PEOPLE. "He's a private person. There was no desire for publicity and Adam regrets that there is some – but [he] can't help it given that he was forced to go to court to assert his rights as a father."

Still, a source close to Lakshmi tells PEOPLE, "One has to question Adam's real motive. If he is not seeking publicity then why did he contact the press when he filed his report?"